Testing for a Unit Root Under Errors with Just Barely Infinite Variance

22 Pages Posted: 27 Oct 2008

See all articles by Nikolaos Kourogenis

Nikolaos Kourogenis

University of Piraeus, Department of Banking and Financial Management

Nikitas Pittis

University of Piraeus - Department of Banking and Financial Management

Date Written: 0000

Abstract

tttThis article investigates the problem of testing for a unit root in the case that the error, {u}, of the model is a strictly stationary, mixing process with just barely infinite variance. Such errors have the property that for every ´ such that 0d´<2, the moments E|u|´ are finite. Under some additional restrictions on the rate of decay of the mixing rates, these errors belong to the domain of the non-normal attraction of the normal law and obey the invariance principle. This in turn implies that there might be conditions under which the usual Phillips-type test statistics for unit roots may still converge to the corresponding DickeyFuller distributions. In such a case, the unit-root hypothesis can be tested within an infinite-variance framework without any modifications to either the tests themselves or the critical values employed. This article derives a necessary and sufficient condition for convergence of the standard test statistics to the DickeyFuller distributions. By means of Monte Carlo simulations, the article also shows that this condition is likely to hold in the case that {u} is a serially correlated, integrated generalized autoregressive conditionally heteroskedastic (IGARCH) process and the standard unit-root tests work well.

Suggested Citation

Kourogenis, Nikolaos and Pittis, Nikitas, Testing for a Unit Root Under Errors with Just Barely Infinite Variance (0000). Journal of Time Series Analysis, Vol. 29, Issue 6, pp. 1066-1087, November 2008, Available at SSRN: https://ssrn.com/abstract=1288881 or http://dx.doi.org/10.1111/j.1467-9892.2008.00596.x

Nikolaos Kourogenis (Contact Author)

University of Piraeus, Department of Banking and Financial Management ( email )

80 Karaoli & Dimitriou Str.
18534 Piraeus, 185 34 -GR
Greece

Nikitas Pittis

University of Piraeus - Department of Banking and Financial Management ( email )

80 Karaoli & Dimitriou Str.
18534 Piraeus, 185 34 -GR
Greece

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